Foldable substrates, foldable apparatus, and methods of making

A foldable apparatus comprising a substrate comprising:

• a substrate thickness defined between a first major surface and a second major surface opposite the first major surface;
• a first portion comprising the substrate thickness, a first compressive stress region extending to a first depth of compression from the first major surface, a second compressive stress region extending to a second depth of compression from the second major surface;
• a second portion comprising the substrate thickness, a third compressive stress region extending to a third depth of compression from the first major surface, a fourth compressive stress region extending to a fourth depth of compression from the second major surface;
• a central portion positioned between the first portion and the second portion, the central portion comprising a central thickness defined between a first central surface area and a second central surface area opposite the first central surface area, a first central compressive stress region extending to a first central depth of compression from the first central surface area, a second central compressive stress region extending to a second central depth of compression from the second central surface area, the first central surface area is recessed from the first major surface by a first distance, and the central thickness is less than the substrate thickness;
• and
• a concentration of lithium oxide at the first central surface area is greater than a concentration of lithium oxide at a central midpoint by from about 0.2 mol % to about 2 mol %,
• wherein the first portion comprises:
• a midpoint midway between the first major surface and the second major surface;
• a concentration of lithium oxide at the first major surface;
• a total concentration of potassium oxide, rubidium oxide, cesium oxide, and francium oxide at the first major surface;
• a concentration of lithium oxide at the midpoint;
• and
• a total concentration of potassium oxide, rubidium oxide, cesium oxide, and francium oxide at the midpoint, and
• wherein the substrate is a glass-based substrate or a ceramic-based substrate, and the central midpoint is midway between the first central surface area and the second central surface area, the central portion comprises:
• a total concentration of potassium oxide, rubidium oxide, cesium oxide, and francium oxide at the first central surface area;
• and
• a total concentration of potassium oxide, rubidium oxide, cesium oxide, and francium oxide at the central midpoint.