I don't know Japanese, but I notice they have a mixture of Hiragana, Katakana, and Chinese characters. Instead of a mixture, could you write a whole article in just one of them? Does this ever occur? Are there any examples if so? If not, why not?
You can, but it's considered unusual at best and incorrect at worst.
Using solely kanji means leaving off all functional morphemes and non-content words, so it's like speak### English ####### ### ## ### function## word#, use### #### ### content word#—#### ##, most## noun# ### verb# ### adjective#. Understandable, with effort, but not at all natural.
Using solely kana conveys pretty much all of the same information as spoken Japanese (with the exception of tone). Since people can understand spoken Japanese, they can also understand pure kana; this is how computer interfaces worked for a long time, since the number of kana is relatively small compared to the number of kanji (so they're easier to implement). However, it's extremely "marked", in linguistic terms—it goes against standard Japanese orthography (writing conventions), and iz ə bit laik raiting Inglish mor fonetiklee. Peepl wil stil əndrstand yoo, bət its not hau reel Inglish-speekrz akchlee rait.
Pure kana are often used in books for children and second-language learners, who might not know all the kanji yet. Pure kanji are not used in any context I know of (at least within Japanese).
In modern times, you would not (with exceptions), as the other answers have pointed out. Historically: yes definitely.
When Chinese characters were first imported, they were used only to write (old; then contemporary) Chinese. Before today’s kana were derived from a certain set of these with the desired pronunciation, this certain set (the Manyogana) had to be defined. But even thereafter, it was possible to write in a Kanbun style, employing only kanji with the word ending markers omitted and particles represented by specific kanji.
Arguably more common and more understandable was the opposite: writing entirely in kana. The most famous example is probably the Tale of Genji. It was written by a woman and at the time only hiragana characters were considered suitable for women. Thus, it was originally written entirely in hiragana.
Kanji: You would not write entirely with Kanji (Chinese characters). As stated in the comments "it would feel archaic or outdated, like using Middle English spellings or something". Nowadays Kanjis do not cover all the words / grammatical functions. A simple example is の for possessive, the corresponding Kanjis are archaic.
If you were to write only with Katakana that would be you only using words from foreign origin. Like:
- "fried potatoes" フライドポテト
- "mineral water" ミネラルウォーター
- "spaghetti" スパゲッティー
Hiragana: If you were to write only with Hiragana that would be for pedagogical purpose. When learning Kanji, they have the Hiragana syllabic version of the Kanji written in tiny Hiragana letters.
But I have heard that they can choose to write a word in another alphabet so as to convey a special connotation to it.
Beginner in learning Japanese, I'd be happily corrected or given more information about my statements.
could you write a whole article in just one of them?
Yes, you could, but it would be considered troublesome for both the reader and the writer.
Does this ever occur?
Almost never. Well, it could be done in a book meant for someone who is learning the language, because students learn (or rather, cram) Kanji over several years of studying Japanese.
If not, why not?
Japanese does not use spaces to separate words. So, using different scripts makes it easier to understand where a new word starts.
Some words would be easier to write using Kanji alone because a Kanji is essentially a pictograph. For example, a phonetically long word could be represented as a single Kanji character.
Historically, Kanji were borrowed from the Chinese language, which is a tonal language whereas Japanese is not. So, the structure of the language itself was a bit different and Kanji alone could not be used to express everything in the language. For example, Japanese has many word endings, changing which cannot be done using Kanji. The word root taberu can be transformed to tabemasu, tabemasen etc, which requires the usage of hiragana.