Hornig’s jewelry—18-karat green and white gold, netted with tourmalines, garnets, amethysts, and topaz—sparkles in display cases at high-end retailers like Bergdorf Goodman and Neiman Marcus. She likens the sale of every necklace or bracelet to a challenge grant. “I give my customers something they want—jewelry—and the next step is to give them a chance to see what they can do for others.”   Those who select an original Joan Hornig design will derive pleasure from the jewelry along with the knowledge that they are helping to make a difference.