Chrometech logo / banner

Example Training Outline for Hard Chrome Plating

Note: The reader is advised that the following information represents only the outline used for a particular ChromeTech training session, and may not be appropriate for other locations or situations, or be accurate when taken out of context with verbal and graphical supplements used at the time.
  1. Why hard chromium?
    1. Part to be plated can benefit from improved properties of deposit
      1. Hardness 1
        1. 950-1200 HV (Vickers) for bright deposits
        2. Can be as low as 300-400 HV for dull deposits
      2. Low friction
        1. Steel on chromium has only 30% of the static friction of babbitt on babbitt 2
        2. Coefficient of friction for chromium on steel = 0.16, for steel on steel = 0.30 3
      3. Wearability 1
        1. Increased life expectancy of plated parts
      4. Chemical / corrosion resistance 4
        1. Resistant to most organic acids, gases, foods, petroleum products, oxygen, moisture, sulfur
        2. Attacked by chlorides (hydrochloric acid or HCL, muratic acid), sulfuric acid, formic acid
        3. Thick deposits required due to microcracks
      5. Non-galling with other metals
        1. Galls when rubbed against itself (poor wettability)
      6. Thermal expansion similar to cast iron and glass 5
      7. Wide temperature range for service applications
        1. Hardness & abrasion resistance unchanged up to 200 deg. C. (392 F.); some reduction up to 400 C. (752 F)
      8. Thermal conductivity
        1. Only copper. silver, and gold conduct heat better 6
      9. Oil retention / lubricity
        1. Microcracks hold oil 7
      10. Ability to restore part to dimensional tolerances
  2. Electrolytic process
    1. Chemical and electrical process
      1. Voltage driven chemical process
    2. Bohr theory of atom useful
      1. Hexavalent chromium ions missing six electrons
      2. Trivalent chromium ions missing three electrons
      3. Needed electrons provided at cathode surface
    3. Some debate in industry over the exact plating mechanism
      1. Difficult to identify because chrome is a strong oxidizing acid 8
      2. Stepwise vs. direct reduction
      3. Role of sulfate debated, may serve to de-passivate substrate at boundary layer
        1. Bright chromium is not deposited with fluoride as only catalyst 9
      4. Radioactive tracer studies have shown that all deposited chromium comes from the hexavalent state, not from trivalent state 10
    4. Cathode reactions 11
      1. Cr2O7- - + 14H+ + 12e- >> 2Cr + 7H2O [Deposition of chromium]
      2. 2H+ + 2e- >> H2 [Evolution of hydrogen gas]
      3. Cr2O7- - + 14H+ + 6e- >> 2Cr3+ + 7H2O [Formation of Cr(III)]
    5. Anode reactions 12
      1. 2H2O >> O2 +4H+ + 4e- [Evolution of oxygen gas]]
      2. 2Cr3+ + 6H2O >> 2CrO3 + 12H+ + 6e- [Oxidation of Cr(III)to Cr(VI)]
      3. Pb + 2H2O >> PbO2 + 4H+ + 4e- [Formation of lead dioxide]
  3. Chemistry
    1. Single-catalyst bath most widely used bath for hard chrome
      1. Inexpensive, generic chemicals
      2. Components
        1. Chromium ions from chromic acid: CrO3
        2. Sulfate ions from sulfuric acid: H2SO4
        3. Water
      3. CrO3 concentration ranges from 28 to 53 oz/gal (W/V), but 33 oz/gal most common
      4. SO4 concentration typically 0.28 to 0.53 oz/gal
      5. Chromic acid-to-sulfate ratio more important than absolute concentration of either
      6. 75:1 to 115:1 typical range for chrome-to-sulfate ratio, with 100:1 most common
        1. Ex. 33 oz/gal CrO3 with 0.33 oz/gal SO4.
      7. Low cathodic efficiency: range is 11-19% (dependent upon current density and tank temperature), ~14% for 2 amp/in2 and 130 F. 13
      8. Low cathodic etch
        1. Minimal masking requirement
        2. Areas that do not require plating can be wetted with chrome, and only need shielding from electrical communication anode
        3. Minimal etch (attack) upon ferrous substrates
      9. Sparsely populated, deep, wide microcracks (50-650 cracks/cm) 14
      10. Lower microhardness than chromium from mixed-catalyst or non-fluoride, high-efficiency bath 15
    2. Mixed-catalyst bath
      1. Made from either generic or proprietary chemicals
      2. Components
        1. Chromium ions from chromic acid: CrO3
        2. Sulfate ions from sulfuric acid: H2SO4
        3. Fluoride ions from hydrofluosilicic acid, or proprietary catalyst
        4. Water
      3. CrO3 concentration ranges from 20 to 40 oz/gal (W/V)
      4. SO4 concentration is typically lower (higher chrome-to sulfate ratio) in fluoride baths than in single-catalyst baths
        1. 180:1 to 240:1 CrO3-to-sulfate ratio typical
      5. Fluoride concentration varies widely
        1. Example of widely used, mixed catalyst bath = 32 oz/gal CrO3, 0.16 oz/gal SO4, 0.30 oz/gal SiF6.16
      6. Higher cathodic efficiency: range is 15-27% (dependent upon current density and tank temperature), ~21% for 2 amp/in2 and 130 F. 17
      7. Higher rates of deposition
      8. High cathodic etch
        1. Significant masking requirement: chemical attack will occur to all areas that are wetted with chrome but are not being plated
        2. Even titanium is not suitable for heaters, cooling coil, etc.
        3. Most etching occurs in low current-density regions
      9. Highly populated, shallow, narrow microcrack structure (550-1650 cracks/cm) 18
      10. Microhardness higher than chromium from single-catalyst bath, but lower than non-fluoride, high-efficiency bath 19
    3. Fluoride-free, high-efficiency bath
      1. Expensive, proprietary chemicals
      2. High cathodic efficiency: ~25%
      3. High rates of deposition: similar to mixed-catalyst bath
      4. Low cathodic etch
        1. Etch is similar to single-catalyst bath
      5. Very highly populated, shallow, narrow microcrack structure (1950-3200 cracks/cm) 20
      6. Higher microhardness than chromium from single-catalyst bath 21
  4. Electrical
    1. Direct current (DC) required for deposition
    2. Alternating current (AC) "Ripple" must be kept minimal
      1. Only batteries have true DC
      2. Some small amount of AC bleeds though with DC from power supplies and generators.
      3. Excess ripple causes dull, soft deposits
      4. Maintain ripple below 5%, based upon following formula:

      5.    % Ripple = (Vac / Vdc) x 100
           where: Vac = voltage RMS AC, Vdc = voltage DC

    3. Oscilloscope should not show any portions of waveform dropping below zero voltage potential
    4. Current interruptions are not well tolerated by chromium plating process
      1. Repeated momentary interruptions (milliseconds) cause dull, soft deposits
        1. Improper or faulty power supply
      2. Resuming plating after longer duration can cause peeled or flaked chrome deposits
    5. Voltage vs. Current Regulation
      1. Voltage-regulated power supplies hold voltage constant during plating cycle
        1. Current will drift with changes in resistance
        2. Examples of voltage-regulated power supplies
          1. Tap switch rectifiers
          2. Manual and motor-driven power supplies
          3. Thyristor (SCR) rectifiers placed in the "constant voltage" mode
          4. Motor-generators
      2. Current-regulated power supplies hold amperage constant during plating cycle
        1. Voltage will drift with changes in resistance
        2. Best for long, unattended plating cycles
        3. Examples
          1. Thyristor (SCR) rectifiers placed in the "constant current" mode
          2. Switch-mode units placed in the "constant current" mode
    6. F. Selecting proper current density
      1. Size and shape of part to be plated
      2. Available amps from power supply
      3. Effectiveness of temperature control for plating bath
        1. Cooling system
        2. Agitation
      4. Bath temperature limitations
        1. Heater capacity
        2. Tank liner
      5. Ampacity of bussing and conductors
      6. Ampacity of racking fixtures
      7. Ampacity of anodes
      8. Plating thickness / plating time
      9. Relationship of plating time, overall cycle time and manpower requirements
      10. 1-6 amp/in2 range, 2-3 amp/in2 common
  5. Typical process steps
    1. Preplate finishing
      1. Welding
      2. Grinding
      3. Polishing
    2. Inspection
    3. Masking
      1. Prevent chromium from depositing in unwanted areas
        1. Paint
        2. Tape
        3. Foils
        4. Sheeting
      2. Conductive masking (aluminum or lead tape /foil ) can prevent edge buildup
    4. Cleaning
      1. Purpose
        1. Achieve chemically clean surface prior to plating
        2. Remove all foreign substances from workpiece
          1. Grease
          2. Oil
          3. Soil
          4. Polishing compound
          5. Occlusions
      2. Various options
        1. Hand cleaning
          1. Cleanser and 3M Scotchbrite pad
          2. Pumice and tampico brush
          3. Minimal energy usage, room temperature
          4. Minimal chemicals usage
          5. Labor intensive
        2. Aqueous spray cleaning
          1. Only for conducive part shapes
          2. Moderate energy requirements - heated caustic
          3. Moderate chemical usage
          4. Low labor requirement
        3. Aqueous immersion cleaning
          1. Soak
          2. Anodic
          3. Cathodic
          4. High energy usage - high temperature
          5. High chemical usage
          6. Minimal labor requirement
          7. Safe for delicate finishes
        4. Ultrasonic
          1. Part size limited to transducer size & energy requirement
      3. Water break test
        1. Look for continuous sheeting action
        2. Lack of water breaks indicates good cleaning
    5. Activation
      1. Purpose
        1. Make surface to be plated active, instead of passive
        2. Willing to accept deposit with good bonding
        3. Encourages complete coverage
      2. Acid dips
        1. Sulfuric
        2. Sulfuric-hydrofluoric
        3. Used when reverse etching is not satisfactory
          1. High strength steels, highly alloyed steels, etc.
          2. Tends to contaminate plating bath
      3. Reverse current activation ("reverse etch")
        1. Reverse current applied to part while immersed in chromic acid
        2. Promotes very high bond strengths - ionic bonding
        3. Optimum degree of etch determined by trial and error
          1. Time
          2. Current density
          3. Temperature
    6. Plating
      1. Determine plating amperage as follows
        1. Determine area of plated surface for cylindrically-shaped objects
          1. dia. x length x , where 3.1416
        2. Select appropriate current density
          1. Available power
          2. Ampacity of conductors, racks & anodes
          3. Temperature considerations
        3. Multiply area (in2) times CD (amps/in2) to get amps
          1. Example: Roll is 18" dia. x 75" long face length.
            Area = 18 x 75 x 3.1416 = 4,241 in2.
            If CD = 2 amp/in2 then current = 4,241 in2 x 2 amp/in2 = 8,482 amps
      2. Determine tank time as follows
        1. Determine mil thickness of chromium required: ex. 0.7 mil
        2. Estimate rate of deposition in mil/hr
          1. A formula for estimating rate of deposition from a single-catalyst bath has been derived by graphing results from hundreds of O.D. parts plated in conforming anodes
          2. Rate = (CD x 0.3) + 0.4, where units for rate are mil/hr and units for current density are amp/in2
          3. Example: if CD = 1.8 amp/in2, then rate = (1.8 x 0.3) + 0.4 = 0.94 mil/hr
        3. Divide thickness by rate to get plating time required
          1. Example:
        4. Previous experience with identical rolls can provide the most accurate value for plating rate of deposition
    7. Rinsing
      1. Purpose: Remove all chromic acid from surfaces of part, racking, masking, etc.
    8. Unracking
    9. Unmasking
  6. Leveling
    1. Unlike chrome, many other metals exhibit True Leveling when deposited
      1. Low areas fill in
      2. Example: copper & nickel underlayment for decorative chromium plating process
    2. Chromium plating exhibits Geometric Leveling
      1. High areas get higher
      2. Low areas get lower
      3. Surface profile typically rougher after plating
      4. Defects in base metal are exaggerated
        1. Defects in base metal may not show up until after chrome plating
  7. Stress
    1. Chromium deposits are stressed in tensile
      1. Causes
        1. Shrinking of chromium deposit as hydrogen gas diffuses away 22
        2. Shrinking of deposit as intermediate chromium hydride structure decomposes 23
      2. Cracking relieves stress
      3. No stress-reducing additives (like nickel bath)
        1. No organic additives can survive in strong oxidizing acid
    2. Many parts are already stressed prior to plating
      1. Caused by mechanical operations such as grinding, cutting, etc.
    3. Additional stress imparted to substrate by plating operation can reduce fatigue limit of part or cause part failure (fracture)
    4. Reduction in fatigue limit for high-strength alloys can be >40%, depending upon hydrogen embrittlement relief temperature24
    5. Baking prior to plating can provide stress relief
    6. Shot peening of substrate prior to plating can help by producing compressively stressed steel surface
  8. Microcrack structure
    1. Cracks are formed when deposits relieve internal stresses
    2. Mixed-catalyst baths have higher microcrack density than single-catalyst baths
    3. Microcrack density increases with increasing sulfate levels 25
    4. Corrosion resistance is reduced when cracks go all the way through the coating to base metal
    5. A microstructure that has a high population of fine cracks has better corrosion resistance than one that has fewer, deep cracks
    6. Oil retention by cracks can improve lubricity
      1. Hydraulic cylinders
    7. Emerging technology - filling cracks with desirable particles 26
      1. Tungsten carbide
      2. Silicon nitride
      3. Silicon carbide
      4. Boron carbide
      5. Industrial diamond
  9. Hardness
    1. Factors which affect hardness
      1. Temperature
        1. Highest deposit hardness occurs at lower temperatures than most platers realize: 100-120 deg. F.
        2. CD must be appropriate
      2. Current density
        1. Current densities too high or too low for tank temperature will decrease hardness
      3. Grain size
        1. Finer grain size produces harder deposits
        2. Mostly a function of chemistry, but can be altered by operational parameters
      4. Impurities
        1. The buildup of bath impurities cause a reduction in deposit hardness
    2. Measuring hardness of electrodeposits
      1. Rockwell or Brinell systems are not well suited for electrodeposits
        1. Indentor too large
        2. Penetration & load requirements not consistent with small dimensions associated with deposit thickness
      2. Vickers or Knoops systems are appropriate for measuring electrodeposit hardness
        1. Small indentor
        2. Penetration & loads okay
      3. Hardness values should only be compared to values from other tests using the same system and same gram loading
  10. Corrosion resistance
    1. Factors which affect corrosion resistance
      1. Type of environment
        1. Attacked by chlorides
      2. Deposit thickness
      3. Number of layers of chromium
        1. Chrome-polish-chrome
      4. Preplate finishing
        1. Smoother is better
      5. Postplate finishing
        1. Filling of cracks by polishing
      6. Microcrack structure
        1. Fine microcrack structure better than coarse
        2. Crack-free chromium best for corrosion resistance, but softer, and does not hold up well to mechanical abuse
      7. Bath contamination
        1. Contaminants reduce corrosion resistance
  11. Bright range
    1. Brightness correlates directly with hardness
      1. Dull, frosty, milky or burnt deposits are softer than bright deposits from same bath
    2. Temperature and current density must be matched
      1. J.B. Mohler's bright range chart is a good indicator
    3. Temperature should not vary by more than 1-2 deg. F
      1. Requires good, automatic cooling system
      2. Requires air agitation to prevent thermal stratification in deep tanks
    4. Current density should be as uniform as possible over plated area
      1. Use of shields, robbers, thieves, conforming anodes, auxiliary anodes, etc.
      2. Use of copper-cored or copper-assisted anodes
  12. Fixturing
    1. Chemical resistance
      1. Copper dissolves quickly when submerged in chromic acid or exposed to chromic acid mists
    2. Ampacity
      1. Undersized conductors cause problems
        1. Voltage drop
        2. Current loss
        3. Thin deposits
        4. Overheating
      2. Copper best: 1000 amp/in2 of cross-sectional area
      3. Aluminum 500-600 amp/in2, depending upon alloy
      4. Steel 120-150 amp/in2
      5. Lead 120-150 amp/in2
  13. Defects
    1. Throwing power
      1. Directly related to chrome-to-catalyst ratio
        1. Better throwing power at 115:1 ratio
        2. Worse throwing power at 75:1 ratio
    2. Burning
      1. Low chromic acid concentration 27
      2. Excessive current density
    3. Treeing
      1. Excessive current density
      2. Excessive trivalent chromium concentration
    4. Pitting
      1. Base metal considerations 28
        1. Pits in substrate
          1. Especially common with cast iron
          2. Porosity
          3. Sulfur inclusions
        2. Inclusions in substrate
          1. Native to parent metal
          2. Forced into metal by grinding or polishing operations
    5. Nodules
      1. Base metal considerations 29
        1. Metallic slivers in substrate
        2. Improper preplate finishing
          1. Grinding
          2. Polishing
          3. Etching
      2. See discussion on roughness
    6. Peeling or blistering
      1. Sign of poor adhesion
      2. Causes
        1. Improper cleaning
        2. Improper reverse etch activation
        3. Oxides, scale, carbon or foreign substance on base metal
        4. Improper chrome-on-chrome procedure
        5. Current interruption during plating
    7. Reduced coverage
    8. Roughness
      1. Metallic contamination of plating bath 30
      2. Improper reverse etch 31
        1. Low degree of reverse etch will not lift steel slivers, resulting in less nodulization & smoother deposits
        2. High degree of reverse etch may lift, then remove slivers, also resulting in smooth deposits
          1. Works best on low-carbon or lightly alloyed steels
          2. Over-etching high carbon steels usually causes roughness from nodule formation where carbon particles were brought to surface
        3. Moderate degree of reverse etch may lift slivers, resulting in rough, nodulous chrome deposits
      3. Excessive current density
    9. I. Hazy deposits
      1. Metallic contamination of plating bath 32
      2. Chloride contamination of plating bath 33
    10. Dull (milky) or soft deposits
      1. Mismatch between temperature and current density
        1. Temperature stratification in plating bath
        2. Inadequate agitation
      2. Improper chromic acid-to-catalyst ratio
      3. Low chromic acid concentration
    11. Poor corrosion resistance
      1. Bath impurities
      2. Improper preplate finishing
        1. Grinding
        2. Polishing
        3. Etching
          1. Reverse etching should remove steel slivers, not just stand them up before plating 34
      3. Surface profile 35
        1. Smoother surface profiles (before and after plating) improve corrosion resistance 36
      4. Unfavorable microcrack structure
  14. Anoding
    1. Conforming anodes
      1. True-to-round deposits
      2. High efficiency
      3. Closer anode spacing
      4. Lower plating voltage
      5. Copper assist to anode bottom
    2. Stick anodes
      1. Potential for out-of-round deposits
      2. Lower efficiency
      3. Farther anode spacing
      4. Higher plating voltage
      5. Copper assist to anode bottom (copper-core)
  15. Plating chrome-on-chrome
    1. Procedure differs from chrome-on-steel
      1. Needed to get good adhesion between new & existing chromium layers
    2. Three requirements
      1. Thoroughly prewarm steel part and existing chromium layer before plating
        1. Both case of steel and chromium deposit should be at bath temperature
      2. Plater must get the proper degree of reverse etch activation on first (old) chrome layer
        1. Too little etch causes peeling between layers
        2. Too much etch degrades lower chromium layer by opening up cracks
        3. Due to differences in condition of underlayment chrome layer, can't always use same number of seconds of reverse etch
        4. Try 60 sec. after significant gassing is observed during reverse etch (2 amp/in2). Adjust subsequent rolls up or down.
      3. Current must be ramped up from a low power setting to normal plating current over a period of several minutes
        1. Begin electrolyzing at a low power setting that is above the hydrogen overvoltage potential, but below the potential at which chromium is deposited
          1. Hydrogen "wash"
          2. Try 3.0 VDC
        2. Begin slowly raising the power uniformily at a rate that will take 7-8 min. to get to normal plating amperage.
        3. Problems with incorrect ramp
          1. Too fast a ramp (or none at all) may result in peeled chrome
          2. Too slow a ramp results in a band of soft chrome between layers, because CD is too low for temperature during early stage of ramp.
  16. Impurities
    1. Trivalent chromium
      1. Formed at cathode: reduction of Cr+6 to Cr+3, instead of Cr+6 to Cr0
        1. Cr+3 will not reduce further to metallic chromium deposits
      2. Also formed when organic matter (oil, grease, dirt, rags, etc.) dissolved in chromic acid
      3. Offset by reoxidization of Cr+3 to Cr+6 at anode surface
        1. Reason that lead-alloy alloys are used for hard chrome plating
      4. Equilibrium concentration determined by net result of these cathode and anode reactions
      5. I.D. plating always results in increase of Cr+3 due to unfavorable anode-to-cathode (surface area) ratio
      6. Adverse effects of high trivalent: > 0.5 oz/gal (3.7 g/L) 37
        1. Increased bath resistivity
          1. Higher voltage needed to get same amps
          2. Longer plating cycles possible
          3. Wasted energy
        2. Increased tendency for burning
        3. Dark banding at end of plated area
        4. Reduced coverage
    2. Metallic impurities
      1. Most common metallic impurities
        1. Fe: Iron from ferrous substrates
          1. Builds up faster in bath when parts are reverse etched in plating tank
        2. Cu: Copper from racks and bussing
        3. Al: Aluminum from racks
        4. Ni: Nickel from nickel plated parts
        5. Zn: Zinc from die castings
      2. Usually grouped together when considering effects
      3. Adverse effects of high metallic contamination: > 1.0 oz/gal ( 7.5 g/L) 38
        1. Increased bath resistivity
        2. Deposit roughness
        3. Hazy deposits
        4. Reduced coverage
        5. Decreased bright range
        6. Can interfere with fluoride catalyst in mixed-catalyst baths
    3. Chlorides
      1. Most worrisome organic contaminant
      2. Very small levels can cause problems
      3. Adverse effects of high chloride contamination: > 0.009 oz/gal (0.07 g/L) 39
        1. Upset catalyst ratio
        2. Reduced coverage
        3. Gray or mottled deposits
        4. Reduced efficiency
        5. Increased cathodic etching of parts
    4. Reducing impurity levels in the bath
      1. Properly dispose of all or part of bath, replace with new
      2. Purification equipment: continuous or batch types
        1. Ion exchange
          1. Proven technology
          2. Generate significant amounts of liquid waste
          3. Fast
          4. Highest purity chrome bath
          5. Cr+3 is added to waste product
        2. Membrane / Electrodialysis
          1. Emerging technology
          2. Minimal waste product - solid form
          3. Slow
          4. Acceptable bath purity levels
          5. Cr+3 is re-oxidized to Cr+6
  17. Hydrogen Embrittlement
    1. Caused by hydrogen gas liberated at cathode during plating
    2. Some gets trapped in chromium matrix as deposition continues
    3. Can result in catastrophic failure of high-tensile steels
      1. Hydrogen embrittlement may cause a loss of ductility in steels that are subjected to slow rates of strain during service
        1. Slow-bend test for ductility
      2. Hydrogen embrittlement may cause delayed fracture of high-tensile steels at abnormally low stress levels
        1. Static-fatigue test for delayed failure
    4. Relieved by post-plate bake
      1. Typ. 350-375 F. for 1-3 hr., but can vary

Footnotes / References:

1 Hard Chromium Plating, R. Guffie, p. 15

2 Ref. 1, p. 17

3 Nickel and Chromium Plating, J. Dennis and T. Such, p. 70

4 Heavy Deposition, J. Greenwood, pp. 144-146

5 Ref. 1.

6 Ref. 1.

7 Ref. 3, p. 70

8 Electroplating, F. Lowenheim, p. 235

9 Ref. 8

10 Ref. 8

11 Ref. 8, p.234

12 Ref. 8, p.234.

13 1994 Metal Finishing Guidebook and Directory, Table III, p. 196

14 "Microcracks in Hard Chromium Electrodeposits", A. Jones, April '89 Plating and Surface Finishing Magazine, Table 2, p. 64

15 Ref. 14

16 Ref. 13, p. 194

17 Ref. 13

18 Ref. 14

19 Ref. 14

20 Ref. 14

21 Ref. 14

22 Ref. 3, p. 160

23 Ref. 3, p. 160

24 Ref. 3, p. 72

25 Ref. 14, p. 66

26 German patent 3,531,410. From "What's New in Surface Finishing", G. Karustis, Feb. '88 Plating & Surface Finishing Magazine, p. 18

27 Troubleshooting Functional Chromium", N. Corriere Jr., AESF Chromium Colloquium, 1994, p. 130

28 Eliminating Substrate Defects", A. Jones, AESF Chromium Colloquium, 1994, p. 99

29 Ref. 28

30 Analytical Methods for Hexavalent Chromium Plating Solutions", M. Traficante, AESF Chromium Colloquium, 1994, p. 121

31 ref. 28, p. 102

32 Ref. 30

33 Ref. 27, p. 131

34 Ref. 28, p. 103

35 Ref. 28, p. 103

36 Ref. 28, p. 103

37 Ref. 30

38 Ref. 30

39 Ref. 30