Dual core golf ball having a shallow “positive hardness gradient” thermoplastic inner core and a steep “positive hardness gradient” thermoset outer core layer

1. A golf ball comprising:

an inner core layer comprising a thermoplastic highly-neutralized ionomer comprising a copolymer of ethylene and an α,β-unsaturated carboxylic acid, an organic acid or salt thereof, and sufficient cation source to neutralize the acid groups of the copolymer by 80% or greater, and having a geometric center hardness less than a surface hardness to define a first hardness gradient;

an outer core layer disposed about the inner core, the outer core being formed from a homogenous thermoset composition and having an interior hardness substantially less than an outer surface hardness to define a second hardness gradient;

an inner cover layer disposed about outer core layer; and

an outer cover layer disposed about the inner cover layer,

wherein the first and second hardness gradients are positive and a slope of the second hardness gradient is greater than a slope of the first hardness gradient.

2. The golf ball of claim 1 , wherein a ratio of the slope of the second hardness gradient to the slope of the first hardness gradient is greater than 1.

3. The golf ball of claim 2 , wherein a ratio of the slope of the second hardness gradient to the slope of the first hardness gradient is greater than 1.5.

4. The golf ball of claim 3 , wherein a ratio of the slope of the second hardness gradient to the slope of the first hardness gradient is greater than 2.

5. The golf ball of claim 1 , wherein the inner core layer has an outer diameter of about 0.5 inches to about 1.13 inches.

6. The golf ball of claim 1 , wherein the first hardness gradient is less than 10 Shore C and the second hardness gradient is greater than 10 Shore C.

7. The golf ball of claim 6 , wherein the first hardness gradient is less than 5 Shore C and the second hardness gradient is greater than 15 Shore C.

8. The golf ball of claim 1 , wherein the acid groups of the copolymer are neutralized by 90% or greater.

9. The golf ball of claim 8 wherein the acid groups of the copolymer are neutralized by about 100%.

10. The golf ball of claim 1 , wherein the organic acid or salt thereof comprises barium, lithium, sodium, zinc, bismuth, chromium, cobalt, copper, potassium, strontium, titanium, tungsten, magnesium, cesium, iron, nickel, silver, aluminum, tin, or calcium salts, or salts of fatty acids.

11. The golf ball of claim 10 , wherein the fatty acid salt comprises stearic acid, behenic acid, erucic acid, oleic acid, linoelic acid or dimerized derivatives thereof.

12. The golf ball of claim 10 , wherein the organic acid or salt thereof comprises a magnesium salt of oleic acid.

13. The golf ball of claim 1 , wherein the outer core layer comprises a soft and fast agent.

14. The golf ball of claim 13 , wherein the soft and fast agent comprises a halogenated thiophenol.

15. A golf ball comprising:

an inner core layer consisting of a thermoplastic material and having a geometric center hardness less than a surface hardness to define a first positive hardness gradient of less than 10 Shore D points;

an outer core layer disposed about the inner core, the outer core being formed from a substantially homogenous thermoset composition comprising a diene rubber and having a second positive hardness gradient of 10 Shore D points or greater;

a cover layer disposed outer core layer, the cover layer comprising an inner cover layer comprising an ionomer and an outer cover layer comprising a castable polyurethane or polyurea material.

16. The golf ball of claim 15 , wherein a ratio of the second positive hardness gradient is greater than the first positive hardness gradient.

17. The golf ball of claim 16 , wherein the ratio is greater than 1.5.

18. The golf ball of claim 17 , wherein the ratio is greater than 2.