Why would pure antifreeze freeze in the plastic bottle beside the radiator and the radiator itself in cold weather while there is no leakage?

Actually, this is to be expected when one considers that ethylene glycol, the principal component of most antifreezes, freezes at 8 degrees above zero, Fahrenheit. It is only when water is added that the freezing point is depressed. The freezing point of an ethylene glycol and water mixture drops rapidly as the concentration of glycol is increased to a mixture of about 60% antifreeze and 40% water. Around that point, an abrupt turnabout occurs, and as more antifreeze is added, the freezing point rises almost as fast as it had previously dropped. It's clearly a case of what you don't know can hurt you, but I have never seen an antifreeze container with an explanatory note to this effect. It must have leakage somewhere. When it gets cold the antifreeze contracs. That is why there is a bottle next to the radiator that has two marks COLD and hot. the level should be in between these. If it is not and way off then you have a leak somewhere. Leak may be small, may be in the hadgasket (no good), look under the car to see if any green or colr fluid is under overnite. Did you unscrew the radiator cap and forget to tighten it roccetly?